The question you opened
Six percent and the rule of 72
Savings sit in an account paying 6% a year, compounded once a year.
By the rule of 72, how many years until the money doubles?
12 years
Divide 72 by the rate: 72 over 6 is 12. The exact figure is 11.9 years, so the shortcut is close enough to say out loud.
Money growing at 6% a year doubles in about 12 years, and you get there by dividing 72 by the rate. That is the entire rule. Why 72 and not 100. Doubling under compound growth is a logarithm question: you need the number of years y such that 1.06 to the power y equals 2. Solving that gives 11.896 years. The rule of 72 gives 12. The error is about one part in a hundred, which is far smaller than your uncertainty about the interest rate itself.
The number 72 is chosen for arithmetic rather than accuracy. It divides cleanly by 1, 2, 3, 4, 6, 8, 9 and 12, which covers almost every rate anyone quotes. At 8% you get 9 years. At 9% you get 8 years. At 4% you get 18 years. At 3% you get 24 years. All of them land within about four months of the exact answer for rates between roughly 4% and 12%. The rule runs backwards too, and that is where it earns its keep.
If a fund tells you it doubled in six years, divide 72 by 6 and you know the rate was around 12% a year. If a country doubled its output in 24 years, that is about 3% growth. One division turns a headline into a rate. It also works for anything that shrinks. Inflation at 3% halves what your money buys in about 24 years. A subscription rising 6% a year costs double in 12. Two cautions.
The rule assumes compounding, so it does not apply to simple interest, where a 6% return doubles your money in about 17 years. And it drifts at extremes: above roughly 20% a year the true doubling time runs longer than 72 divided by the rate, so the shortcut promises more than it delivers. Inside the ordinary range it is one of the few pieces of finance you can do at a dinner table without reaching for anything.
Technique: Rule of 72